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Math Help - Mapping vector spaces

  1. #1
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    Mapping vector spaces

    Hi!

    I have a problem with this math task:

    Linear transformation maps basic vectors to vectors (2,−3,−5), (0, 4, 8) and (2, 9, 2).
    In which vector (vx, vy, vz) does vector (-3, 9, -1) maps?


    (sorry for my BAD English)
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  2. #2
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    Quote Originally Posted by T-Mac View Post
    Hi!

    I have a problem with this math task:

    Linear transformation maps basic vectors to vectors (2,−3,−5), (0, 4, 8) and (2, 9, 2).
    In which vector (vx, vy, vz) does vector (-3, 9, -1) maps?


    (sorry for my BAD English)
    I do not understand the problem.
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  3. #3
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by T-Mac View Post
    Hi!

    I have a problem with this math task:

    Linear transformation maps basic vectors to vectors (2,−3,−5), (0, 4, 8) and (2, 9, 2).
    In which vector (vx, vy, vz) does vector (-3, 9, -1) maps?


    (sorry for my BAD English)
    You are looking for a linear transformation L that takes
    L(2, -3, -5) = (0, 4, 8)
    L(0, 4, 8) = (2, 9, 2)

    and looking for the vector v = (vx, vy, vz) such that
    L(vx, vy, vz) = (-3, 9, -1)

    Is this correct?

    -Dan
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  4. #4
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    topsquark, yes.
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  5. #5
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by T-Mac View Post
    Hi!

    I have a problem with this math task:

    Linear transformation maps basic vectors to vectors (2,−3,−5), (0, 4, 8) and (2, 9, 2).
    In which vector (vx, vy, vz) does vector (-3, 9, -1) maps?


    (sorry for my BAD English)
    now i'm a little rusty on linear algebra, so correct me if i'm wrong. you said topsqaurk was right, so we are given that:
    L(2, -3, -5) = (0, 4, 8)
    L(0, 4, 8) = (2, 9, 2)

    however, the standard matrix for L will be a 3x3 matrix, and therefore, we need at least 3 examples of transformations to find it.

    unless there was some other way which i am not remembering at the moment
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